Either Arithmetic and Logic Are Both Necessary or Logic and Geometry

question 217

Multiple Choice

Either arithmetic and logic are both necessary or logic and geometry are both necessary. If all knowledge is experiential, then even logic is not necessary. So, not all knowledge is experiential.
-Which of the following is the best translation into PL of this argument?

• A) (A • L) \( \lor \) (L • G) E ⊃ ∼L / ∼E
• B) N \( \lor \) ∼N E ⊃ L / ∼E
• C) (A \( \lor \) L) • (L \( \lor \) G) E ⊃ ∼L / ∼E
• D) N \( \lor \) ∼N E ⊃ ∼L / ∼E
• E) (A • L) \( \lor \) (L • G) E ⊃ L / ∼E

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